Estimate the value of cos 2??

We know that trigonometric ratios can be expressed in terms of π. Let us now find the value of cos2π.

Solution

π is denoted for 180°, which is half of the rotation of a unit circle.

Hence, 2π denotes full rotation.

So, for any number of a full rotation, n, the value of cos will remain equal to 1

we know that, cos 0° = 1

Now, once we take a complete rotation in a unit circle, we reach back to the starting point.

After completing one rotation, the value of the angle is 360° or 2π in radians.

Thus, we can say, after reaching the same position,

Cos 0° = cos 360°

Or

Cos 0° = 2π

Therefore, we conclude that,

Cos 360° = cos 2π = 1

Answer

cos 2π = 1

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